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Form the differential equation of the family of curves y = a sin (x + b), where a and b are arbitrary constants.

OR

Solve the following differential equation:

2xydx + (x2 + 2y2) dy = 0

Asked by Topperlearning User 4th June 2014, 1:23 PM
Answered by Expert
Answer:

y = a sin (x + b) ….(1)

Differentiating both sides of equation (1) with respect to x,

y' = a cos (x + b) ...(2)

Differentiating equation (2) with respect to x,

y'' = -a sin (x + b) ...(3)

From equations (1) and (2), we obtain,

y'' + y = 0

This is the required differential equation.

OR

2xy dx + (x2 + 2y2) dy = 0

Thus, the given differential equation is a homogeneous equation.

Substitute y = vx

Substituting the values of y and in equation (1), we obtain

Integrating both sides, we obtain

Answered by Expert 4th June 2014, 3:23 PM
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